HP 17BII and HP 17BII+: Finance Solver Equations

HP 17BII and HP 17BII+:  Sales Tax, Substantial Presence Test, Automobile Purchase, Principal Interest Property Tax & Insurance (PITI), Retirement Accounts

Note:  Some equations have the L (Let) and G (Get) functions, which are not available on the brown keyboard of the 17BII+ (around 2003). 

Sales Tax:  Determine the total amount of taxable items and non-taxable items.

AMT=NTAX+TXBL*(1+R%÷100)

AMT:  Total Amount
NTAX:  Items not subject to sales tax
TXBL:  Items subject to sales tax
R%:  sales tax rate

Example 1:  A company purchases equipment which costs $99.99, which was subject to 9.5% sales tax, which includes $139.99 of services.  The services are not subject to sales tax.  What is the total invoice? 

Input:
NTAX:  139.99
TXBL: 99.99
R%:  9.5(%)

Output:
AMT = 249.48

The total of the invoice is $249.48.

Example 2:  During an audit, a company finds an invoice with the total of $236.40 (amount), and the invoice listed non-taxable services of $146.50.  The company lives in a county where the sales tax is 8.75%.  What is the amount of taxable items? 

Input:
NTAX:  146.50
R%:  8.75(%)
AMT:  236.40

Output:
TXBL = 82.67

The amount of taxable items on the invoice is $82.67.

Substantial Presence Test

For more information about the substantial presence test, please click here:  http://edspi31415.blogspot.com/search?q=substantial+presence+

This equation uses Let and Get. 

SPT=IF(L(X:DDAYS(D:12.31+FP(100*D)÷100:1)>183:DATE(D:183):DATE(1.01+(FP(100*D)+.0001)÷100:IP(183-G(X)÷3)))

STP:  Number of days calculated for the Substantial Presence Test
D:  Date (in the format DD.MMYYYY)

Example 1:

D:  1.052019 (1/5/2019),  SPT = 7.072019 (7/7/2019)

Example 2:

D:  6.182008 (6/18/2008), SPT = 12.182008 (12/18/2008)

Example 3:

D:  9.262018 (9/26/2018), SPT = 6.012019 (6/1/2019)

Example 4:

D:  7.102017 (7/10/2017), SPT = 5.062018 (5/6/2018)

Financing the Purchase of an Automobile

This equation deals with the purchase of an automobile. 

AUTO:PRICE*(1-DISC%*.01)*(1+STAX%*.01)-DOWN=PMT*USPV(I%÷12:YRS*12)

PRICE: Sticker price of the automobile
DISC%:  Discount percent
STAX%: Sales tax rate
DOWN:  Down payment (amount)
PMT:  Payment of the loan
I%:  Interest rate of the loan
YRS: Number of years of the loan

Example 1:  The sticker price of a car is $28,000.00.  A discount of 15% is offered.  The car is subject to 10% sales tax.  The dealer offers a 6-year loan at 4.5%.  With $2,000, what is the monthly payment?

Input: 
PRICE: 28000.00
DISC%: 15
STAX%:  10
DOWN: 2000
I%:  4.5
YRS: 6

Output:
PMT = 383.83

The monthly payment is $383.83. 

Example 2:  Assuming the same facts from Example 1, expect the buyer wants to pay no more than $350.00 a month.  What is the required down payment?

Input: 
PRICE: 28000.00
DISC%: 15
STAX%:  10
I%:  4.5
YRS: 6
PMT: 350.00

Output:
DOWN = 4131.42

The down payment needs to be $4,131.42.

Real Estate:  Principal Interest Property Tax & Insurance (PITI)

Determine the total payment of mortgage when considering property tax and property insurance. 

PITI=MORT÷USPV(I%÷12:YRS*12)+(PROP$+INS$)÷12

PITI:  Payment including principal, interest, property tax, and insurance
MORT:  Mortgage amount, price of the property
I%:  Annual interest rate
YRS: Number of the years of the mortgage
PROP$:  Annual property tax
INS$:  Annual property insurance

Example:  A buyer purchases a home with a price of $200,000.00.  The amount is to be financed.  The loan lasts for 30 years and 5% interest rate.  There is annual property tax of $1,200.00 with insurance of $395.95.  What is the buyer's PITI?

Input:
MORT: 200000.00
I%:  5
YRS: 30
PROP$:  1200.00
INS$:  395.95

Output:
PITI = 1206.64

The buyer's PITI is $1,206.64. 

Retirement Accounts:  Future Value and Earned Untaxed Dividends

Determine the future value and untaxed dividends of tax-free retirement accounts (IRS/Keogh).

There are two versions, the second uses Let (L) and Get (G) functions.

Version 1:
IRA: VAL*0+DIV*0+IF(S(VAL):USFV(I%:YRS)*PMT*(1+I%÷100)-VAL:0)+IF(S(DIV):(USFV(I%:YRS)*(1+I%÷100)-YRS)*PMT-DIV:0)

Version 2:
IRA:(VAL+DIV+L(X:USFV(i%:YRS)*(1+I%÷100)))*0+IF(S(VAL):G(X)*PMT-VAL:(G(X)-YRS)*PMT-DIV)

Input Variables:
I%:  Annual Interest Rate
YRS:  Number of Years
PMT:  Annual Payment

Output Variables:
VAL:  Tax Free Value of the Retirement Account
DIV:  Total Untaxed Dividends Earned

Remember, these are untaxed amounts.

Example:
I%:  6.88
PMT:  1000.00
YRS: 40

Output (Results):
VAL = 206811.01
DIV = 166881.01

Source:
Tony Hutchins, Luiz Vieria, and Gene Wright "HP 12C Platinum Solutions Handbook"  Hewlett Packard.  Revised 03.04  2004

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

HP Prime: Two Port Network Transistor Configuration Conversions (h-Parameter Conversions)

HP Prime: Two Port Network Transistor Configuration Conversions (h-Parameter Conversions)

Introduction

The program TRCONV converts h-parameter matrices for the following configurations of two-port networks:

*  Common Base Transistor Configuration (CB)
*  Common Emitter Transistor Configuration (CE)
*  Common Collector Transistor Configuration (CC)

The h-parameter matrix, also known as a hybrid parameter, is a 2 x 2 matrix representation of a two port network. 

H = [ [ h11,  h12 ] , [ h21, h22 ] ] where:

[ [ V1 ], [ I2 ] ] = = [ [ h11,  h12 ] , [ h21, h22 ] ] * [ [ I1 ], [ V2 ] ]

The h-parameter matrix takes into account the short circuit condition (h11, h22) and the open circuit condition (h12, h21) in the two port network. 

The dimensions of the entries are:

h11:  input impedance, in ohms (Ω)
h12:  reverse voltage gain, dimensionless
h21:  forward current gain, dimensionless
h22:  output admittance, in seimens or mhos (1/Ω)

The resulting matrix from TRCONV is known as a y-parameter matrix. 

HP Prime Program TRCONV

EXPORT TRCONV()
BEGIN
// 2019-03-10
// HP 67
LOCAL h11,h12,h21,h22;
LOCAL y11,y12,y21,y22;
LOCAL w1,w2,w3,w4,w5;
LOCAL t,l;

l:={"CE→CB","CB→CE","CC→CB",
"CB→CC","CC→CE","CE→CC"};

INPUT(
{{h11,[[0],[3]]},
{h12,[[0],[3]]},
{h21,[[0],[3]]},
{h22,[[0],[3]]},
{t,l}},
"TRANSISTOR CONVERSION",
{"h11: ","h12: ","h21: ",
"h22: ","Type:"}
);

y11:=1/h11;
y12:=−h12/h11;
y21:=h21/h11;
y22:=(h11*h22-h12*h21)/h11;

MSGBOX([[y11,y12],[y21,y22]]);

w1:=y11+y12+y21+y22;
w2:=−(y12+y22);
w3:=−(y21+y22);
w4:=−(y11+y12);
w5:=−(y11+y21);

IF t==1 OR t==2 THEN
RETURN [[w1,w2],[w3,y11]];
END;

IF t==3 THEN
RETURN [[y22,w3],[w2,w1]];
END;

IF t==4 THEN
RETURN [[w1,w5],[w4,y11]];
END;

IF t==5 OR t==6 THEN
RETURN [[y11,w4],[w5,w1]];
END;

END;

Example:

H = [ [ 150, 0.003 ], [ 68, 0.007 ] ]

CE → CB:  [ [ 0.46562, -0.00562 ], [ -0.458973333333, 6.666666667E-3 ] ]

CC → CE: [ [ 6.666666667E-3, -6.646666667E-3 ], [ -0.46, 0.46562 ] ]

Source: 

"5. Transistors Configuration Conversion"  HP 67-97 E.E. Pac I.  Hewlett Packard.  1976

"h Parameter or Hybrid Parameter of Two Port Network" Electrical Concepts.  2019  https://electricalbaba.com/h-parameter-hybrid-parameter-two-port-network/  Retrieved March 21, 2019


Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

DM 41L: A Song of Irrational Numbers

Tones of the first ten digits of the constants π, √2, Zeta(2), Phi (Golden Ratio constant), and e (Euclidean constant) using the Swiss Micros DM 41L

https://youtu.be/aCLT6lzvnS0

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

Algebra: Solving Simple Non-Linear Systems

Algebra: Solving Simple Non-Linear Systems

System I:  

x + y = a
x^2 + y = b

Solving for y:
x + y = a
y = a - x

Subtracting the two equations from the system:
x + y = a
- [x^2 + y] = -[ b ]

x - x^2 = a - b
x^2 - x = b - a
x^2 - x - (b - a) = 0

Solving for x:
x = ( 1 ± √(1 - 4*(b - a) ) / 2

Summary for System I:
x = ( 1 ± √(1 - 4*(b - a) ) / 2
y = a - x

If a and b are real numbers, then 1 - 4*(b - a) ≥ 0, and
1 ≥ 4*(b - a)

System II:

x + y = a
x + y^2 = b

Solving for x:
x + y = a
x  = a - y

Subtracting the two equations from the system:
x + y = a
- [ x + y^2 ] = -[ b ]

y - y^2 = a - b
y^2 - y = b - a
y^2 - y - (b - a) = 0

Solving for y:
y = ( 1 ± √(1 - 4*(b - a) )/2

Summary for System II:
x  = a - y
y = ( 1 ± √(1 - 4*(b - a) )/2

System III:

x + y = a
x^2 + y^2 = b

Solving for y:
y = a - x

Solving for x:
x^2 + (a - x)^2 = b
x^2 + a^2 - 2*a*x + x^2 = b
2*x^2 - 2*a*x + (a^2 - b) = 0

x = ( 2*a ± √(4*a^2 - 4*2*(a^2 - b) ) / 4
x = ( 2*a ± √(4*a^2 - 8*(a^2 - b) ) / 4
x = ( 2*a ± √(4*a^2 - 8*a^2 + 8*b) ) / 4
x = ( 2*a ± √(8*b - 4*a^2) ) / 4
x = ( a ± √(2*b - a^2) ) / 2

Summary for System III:
x = ( a ± √(2*b - a^2) ) / 2
y = a - x

System IV:

x^2 + y^2 = a
x * y = b

Solving for y:
y = b / x 

I'm assuming that x ≠0 and y ≠0.

x^2 + y^2 = a
x^2 + (b / x)^2 = a
x^4 + b^2 = a * x^2
x^2 - a * x^2 + b^2 = 0

Let w = x^2, then w^2 = x^4

Then:
w^2 - a*w + b^2 = 0

Then:
w = (a ± √(a^2 - 4 * b^2) )/ 2

And:
x = ± √( (a ± √(a^2 - 4 * b^2) )/ 2 )

We have four answers to the system.

Summary for System IV:
x = ± √( (a ± √(a^2 - 4 * b^2) )/ 2 )
y = b / x 

A lot of fun,

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

Birthday Blog: Fun Facts About Me

Fun Facts About, me, Eddie Shore, the author of Eddie's Math and Calculator Blog:

1.  I have a Bachelor's Degree in Accounting and a Master's Degree in Mathematics, both from Cal Poly Pomona.

2.  I don't have a favorite sport.

3. My favorite video games are Super Mario Maker, Super Mario Brothers, Mario Kart, Millipede, and Joust.

4. My favorite colors are sky blue, denim blue, forest green, and gold.

5. For you zodiac fans, my zodiac sign is Pisces.  Both of my parents are Geminis, and most of my closest friends are Scorpios.

6. Chocolate chip cookies are my weakness.

7. My four favorite go-to music artists are Earth, Wind & Fire, Stevie Wonder, Janet Jackson, and Sheryl Crow.

8. At home, I have two dogs and three cats. 

9.  I'm Irish and Mexican.

10.  Every morning I write what I want to accomplish for the day.  I go through a lot of Post-Its.

11. The beach is my sanctuary.

12. The mathematics section of university library is to me what Disneyland is to most people, only I don't have to pay $60 for an admission ticket. ;)  My favorite library is the Honnold Mudd Library in Claremont (Claremont Colleges).

13. I can't live without music.  Or calculators.

14. My dream car is a Ferrari. 

15. I prefer tea over coffee.

16. My turn ons are honesty, warmth, kindness, intelligence, and a love for life.

17. My turn offs are dishonesty, arrogance, racism, sexism, and ageism.

18. My bucket list grows by the day.

19. I am very close to my family. 

20. My favorite vacation spot so far is Maui.

21. My favorite number is pi (π), partly because my birthday is March 14 (the day that this blog is posted).

22. I want to go to Greece, Italy, Ireland, and New Zealand.  I'd probably wouldn't return home. 

23. My guilty pleasure is the Real Housewives of New Jersey.  #TeamMargaretJosephs

24. I'm nearsighted and prefer glasses to contacts.

25. I prefer wine over beer, but I do enjoy a good ale.  My favorite shot is Fireball.

26. My newest favorite YouTube channel is Doctor Mike. Favorite of all time is both Cinemasins and Music Video Sins.

27. My favorite calculators are the HP Prime, HP 42S, HP 12C, TI-84 Plus CE and Casio fx-991EX.

28. I am a Press Your Luck addict. Big Bucks, no whammies!

29. I have two dogs and three cats.

30. My music tastes are kind of eccentric, but I learn towards rock, alternative, and some R & B.  I do have a Spotify account. 

31.  My favorite fruits of cherries, applies, and strawberries.

32.  My favorite holiday used to be Christmas, now it's Halloween.

33.  A hobby I like but don't do enough of is art.  I'm drawn to glass art, mythological art, and fantasy art. 

34.  My favorite movie is Ghostbusters - the 1984 original one.

35.  My favorite pie is apple. 

36.  My favorite fonts are Arial, Courier, Futura, and Banschrift.

37.  I lived in Southern California all my life.

38.  Starting and writing on this blog is one of the most fun things I am very fortunate to do, and I thank you for reading and supporting this blog. 

Eddie
All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

TI-84 Plus: Greenwich Mean Sidereal Time Estimate

TI-84 Plus:  Greenwich Mean Sidereal Time Estimate

Introduction

The program GMST calculates and estimates the Greenwich Mean Sidereal Time for any dates between January 1, 1900 and December 31, 2099.

For any date between 1900 and 2099, the date number is calculated as:

number of days since January 1 + (year - 1900) * 365 + int((1900 - year)/4) + 0.5 + hour/24

Please keep in mind, the formula in this program is from 1978 (see source).

For the hour, a 2400 hour clock format is used.  For example, 1 AM = 1, 1 PM = 13. 

This program does not take the location of the observer into account.

TI-84 Plus Program: GMST

"2019-03-08 EWS"
Disp "1900-2099"
Input "MONTH: ",M
Input "DAY: ",D
Input "YEAR: ",Y
Input "HOUR: ",H
If fPart(Y/4)=0 and Y≠1900
Then
1→L
Else
0→L
End

If M≥3
Then
int(30.6*M+1.6)+D-35+L→T
Else
int(30.6*M+368.8)+D-400→T
End

T+(Y-1900)*365+iPart((Y-1900)/4)+.5+H/4Z
Z/36525→Z
6°38'45.836"+2400.051262*Z+0°0'0.0929"*Z²→E
24*fPart(E/24)→E
Disp "GMST: ",E>DMS


Example:

Example 1: 

January 1, 1978, Midnight (Hour = 0):  6°41'9.836"

Example 2:

March 13, 2011, 7:00 PM (H = 19): 11°23'54.646"

Source:

Jones, Aubrey  Mathematical Astronomy With a Pocket Calculator  Halsted Press:  John Wiley & Sons, New York.  1978.  ISBN 0 470 26552 3

Eddie


All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

TI-84 Plus and HP 41C: Number of Days After January 1

TI-84 Plus and HP 41C:  Number of Days After January 1

Introduction

The program DATENO calculates the number of days from January 1.  The program prompts whether we are working in a leap year or not. 

With D = Day and M = Month, the days between January 1 and any other date within the calendar year is:

If M = 1 and M = 2 Then
DATE# = int(30.6 * M + 368.8) + D - 400

Otherwise,
DATE# = int(30.6 * M + 1.6) +D - 35  (non-leap year)
DATE# = int(30.6 * M + 1.6) + D - 34  (leap year)

TI-84 Plus Program: DATENO

"DAYS AFTER JANUARY 1"
"2019-03-07 EWS"
Input "MONTH: ",M
Input "DAY: ",D
Disp "0:NO, 1:YES"
Input "LEAP YEAR? ",L
If M≥3
Then
int(30.6*M+1.6)+D-35+L→T
Else
int(30.6*M+368.8)+D-400→T
End
Disp T

HP 41C/DM 41L Program:  DATENO

(^T:  beginning of an alpha string)

01 LBL^T DATENO
02 ^T MONTH
03 PROMPT
04 STO 01
05 ^T DAY?
06 PROMPT
07 STO 02
08 ^T LEAP? N=0,L=1
09 PROMPT
10 STO 03
11 RCL 01
12 3
13 X<=Y?
14 GTO 00
15 30.6
16 RCL 01
17 *
18 368.8
19 +
20 INT
21 RCL 02
22 +
23 400
24 -
25 GTO 01
26 LBL 00
27 RCL 01
28 30.6
29 *
30 1.6
31 +
32 INT
33 RCL 02
34 + 
35 35
36 - 
37 RCL 03
38 + 
39 LBL 01
40 STO 04
41 END

Examples

Days between January 1 and February 16  (M = 2, D = 16):  46

Days between January 1 and October 1 (M = 10, D = 1):
(Non-leap year):  273
(Leap year): 274

Eddie

All original content copyright, © 2011-2019.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.